Question

In: Finance

4. Assume there are three possible future states for the economy (Boom, Stagnant, and Recession) with...

4. Assume there are three possible future states for the economy (Boom, Stagnant, and Recession) with associated probabilities of 20%, 45%, nd 35%. For each future stae of the economy, a security pays either $40.00 or $20.00 with equal probability (i.e., a 50% chance of either payoff occuring).

a. What is the expected future cash flow for any given future state of the economy?

b. What is the expected future cash flow for the security?

c. Further assuming the future outcomes are one year into the future, what is the current price of the security assuming a 5% annual discount rate?

d. What is the conditional expected cash flow for each future state of nature? (Note: It will be the same for each state.)

e. Assuming the given any future state of nature, the $40.00 payoff is Event 1, and the $20.00payoff is event 2. What is the "conditional mean-zero idiosyncratic component" for the security based on the future payoffs in Event 1 and Event 2? (Note: It will be the same for each state.)

f. What is the CAPM beta for this security?

Solutions

Expert Solution

a. The expected future cash flow for any given future state of the economy is calculated by multiplying the cash flow with the probability of its occurrence.

In the given case, since the cash flow can be $40 or $20 with equal probability irrespective of the future state, the expected future cash flow is = 40*0.5 + 20*0.5 = $30.

$30 is the expected cash flow for any of the given future state.

b. The expected future cash flow for the security is calculated by multiplying the expected cash flow for each state with the probability of their occurrence and then adding them up.

For each future state, the expected cash flow is $30.

Therefore, expected future cash flow for the security is $30*0.2 + $30*0.45 + $30*.35 = $6 + $13.5 + $10.5 = $30.

The expected cash flow for the security is $30.

c. Current price of the security = Future value of the security/(1 + discount rate)^n where n is the number of years.

In the given case, the future value of the security is $30 as calculated in part b.

Current price = $30/1.05 = $28.57.

d. For the Boom state, the expected cash flow = $40*0.5 + $20*0.5 = $30.

For the stagnant state, the expected cash flow = $40*0.5 + $20*0.5 = $30.

For the recession state, the expected cash flow = $40*0.5 + $20*0.5 = $30.

The expected cash flow in each of the three states is same as because the cash flow is same and does not depend on the type of future state.

jeff jeffy answered 2 years ago
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